RNA Structural Motifs

RNA Structural Motifs:

Tetraloop (Figure S5a) is a hairpin loop consisting of four consecutive nucleotides and caps a helix.

Its sequence has three common patterns: GNRA, UNCG and CUUG, where N represents any nucleotide and R represents a purine. There are two variants of this motif other than the standard one: with deletion and with insertion, the sequences of which contain three and five nucleotides respectively.

Sarcin/ricin loop (Figure S5b) contains nine nucleotides which belong to two strands. It forms a helix-like structure in which there is a triple base pair. Two consecutive residues on one strand form a cis Hoogsteen/sugar edge interaction. Then one of them forms a base pair (often a Watson-Crick base pair) with a residue located on the other strand. Among all nine nucleotides, five non-canonical base pairs compose the core of the loop. Sarcin/ricin loop is essential for protein binding and assembly of the functional core of the 50S ribosomal subunit (García-Ortega et al. 2010; Lancaster et al. 2008).

Kink-turn, also called k-turn, is a motif which contains ~15 nucleotides. It has two variants: local k- turn (Figure S5c) and composite k-turn (Figure S5d). Both local and composite k-turns have a similar characteristic strand which bends at the position of an internal loop with its direction changed by ~120˚

(the colored strands in Figure 5c and Figure 5d). The characteristic strand is coupled with other strand(s) to form two helices. For local k-turn, the characteristic strand is coupled with only one strand.

On the other hand, for composite k-turn, its characteristic strand is coupled with two strands.

π-turn (Figure S5e) has a similar structure as the characteristic strand of a k-turn. It is formed by a strand which also bends at the position of an internal loop with its direction changed by ~120˚. The difference between a π-turn and a k-turn lies in the size of the internal loop. The internal loop in a k- turn contains three nucleotides. In contrast, there is only one nucleotide in the internal loop of a π-turn.

Besides, a π-turn forms a π shape with respect to its backbone.

Ribose zipper (Figure S5f) is a motif in which four nucleotides from two strands form two sugar edge/sugar edge interactions, so that two strands can approach each other in the form of a zipper.

Least-squares distance between two representative structures:

Suppose two RNA substructures, X and Y, are represented by two sets of 3D points {x1,x2,…,xn} and

{y1,y2,…,yn} (i.e. backbone atoms and base centers from X and Y respectively). X and Y both consist of n points and each point is represented by a 3×1 column vector. The least-squares distance dLS between

X and Y can be formally described as:

n (S1) 2 2 dLS =min xi - ( SR ( y i ) + t ) S, R ,t i=1 where S is a scale factor, R is a rotation matrix, and t is a translation vector. Eq. (S1) indicates that the

distance between two point sets (X and Y) is the smallest sum of distances between points of X and YS,R,t,

where YS,R,t = {SR(yi)+ t}i=1,…,n is the set of new coordinates of Y after a similarity transformation.

The optimal solution of S, R, and t for Eq. (3) is:

n (S2) 2 x'i T , i=1 , R= VU S = n t = x- SR( y ) 2 y'i _ _ i=1

In Eq. (S2), x and y are the centroids of X and Y. Matrices U and V are obtained by singular value

T T decomposition: Y'X' =UΣV , where X' = {x'i}i=1,…,n and Y' = {y'i}i=1,…,n are obtained by subtracting x and y

_ _ from the points, i.e. x'i = xi - x and y'i = yi - y, i = 1,…,n. Details of this optimal solution can be found in

(Arun et al. 1987).

Reference Arun KS, Huang TS, Blostein SD. 1987. Least-squares fitting of two 3-D point sets. IEEE Trans

Pattern Anal Machine Intell 9: 698-700.

García-Ortega L, Alvarez-García E, Gavilanes JG, Martínez-del-Pozo A, Joseph S 2010. Cleavage of the sarcin-ricin loop of 23S rRNA differentially affects EF-G and EF-Tu binding. Nucleic Acids Res 38:

4108-4119.

Lancaster L, Lambert NJ, Maklan EJ, Horan LH, Noller HF. 2008. The sarcin-ricin loop of 23S rRNA is essential for assembly of the functional core of the 50S ribosomal subunit. RNA 14: 1999-2012.